A nonlocal phase-field model with nonconstant specific heat

We prove the existence, uniqueness, thermodynamic consistency, global boundedness from both above and below, and continuous data dependence for a solution to an integrodifferential model for nonisothermal phase transitions under nonhomogeneous mixed boundary conditions. The specific heat is allowed to depend on the order parameter, and the convex component of the free energy may or may not be singular.